Qualitative counting closed geodesics
Abstract
We investigate the geometry of word metrics on fundamental groups of manifolds associated with the generating sets consisting of elements represented by closed geodesics. We ask whether the diameter of such a metric is finite or infinite. The first answer we interpret as an abundance of closed geodesics, while the second one as their scarcity. We discuss examples for both cases.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.11237
 Bibcode:
 2019arXiv190411237K
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Group Theory;
 Mathematics  Geometric Topology
 EPrint:
 10 pages